nirujjhatī is the final fruit of Kusala Mula P.S via the noble eightfold path, which can be described as Parinibbana, and ‘eternal pause of arising/accumulating pañcakkhandhā’.
uppajjāti means Newborn in certain Bhava (human, hell being, god), and the phenomenon depends on Akusala Mula P.S. With that context, uppajjāti indicates ‘endless suffering on the samsara journey clinging on Happy-bhava (considered as nicca/sukha/atta saññā via Avijja).’
jātiyā sati is the word that indicates ‘born (jāti) in the certain mindset’, along with Wrong Interest/Attention ( Micchā Sati ) based on bad San.
Of course, ‘sati’ in jātiyā sati doesn’t refer to ‘sati cetasika (mindfulness to wholesome teaching including Buddha Dhamma)’.
‘sati’ in jātiyā sati means unwholesome attention.
To add a bit more: “Sati” required to get to nirujjhatīis “Sammā Sati,” i.e., to contemplate the anicca, dukkha, anatta nature with the comprehension of Four Noble Truths/Paticca Samuppada/Tilakkhana.